Withdrawal of US forces from Iraq

"We are the keepers of this legacy, guided by these principles once more, we can meet those new threats that demand even greater effort, even greater cooperation and understanding between nations. We'll begin to responsibly leave Iraq to its people and forge a hard- earned peace in Afghanistan."

— Barack H. Obama
44th U.S. President In his Inauguration Day Speech

During my early teenage years, I conducted, almost instinctively, a personal study of Islam, Judaism and Christianity, and made a discovery that was 'profound', at least to me, at that time: Those three religions are more similar than they are different. In fact, they can almost be regarded as scattered fragments of a whole, and when you unify certain scriptures and teachings from the three separate religions, you come-up with a rich holistic treatise on any 'spiritual' subject matter. Strikingly, all three religions can be condensed and be summed-up as: 'Love leads to God'.

Excited, I presented my findings to my father, who then told me that my discovery was nothing new. It in fact, was the mantra of a poorly-groomed generation of liberal twenty-somethings during the 70s; which wholly dedicated its life-energy to illegal 'pharmacological' products, 'free-love', and having a transformative effect on the world: hippies. Of course, I knew about hippies, but then, I only viewed them as placard-wielding people who fought mammoth (sometimes worthwhile) 'battles' in the wrong way - and was incensed by the fact that they had discovered MY discovery before I had discovered it. If I had also known that Universal Unitarianism's founding principle was embedded in MY discovery, I would have thought that my philosophical mulling had been an entire waste of time - as it yielded no new insights. Therefore, I'm glad that I was ignorant about Unitarian Universalism.

Anyway, when I was conducting that study, something else mystified me, and it was Ecclesiastes 1 verses 9 - 11 (from The Christian Holy Book - The Bible) which says (this is according to the English version of The Good News Bible): "What has happened before will happen again. What has been done before will be done again. There is nothing new in the whole world. 'Look', they say, 'here is something new!' But, no it has all happened before, long before we were born. No one remembers what has happened in the past, and no one in the days to come will remember what happens between now and then." That was a bold assertion that needed to be tested, but that would have been too time consuming, so I just left the philosophical mulling in suspended animation and got back to living life like a normal adolescent.

With the passage of time, my knowledge on historical events naturally expanded, and I saw a discernible pattern through time: current events are only distorted mirror reflections of events that precipitated in the past. Hence, my new insights on the repetitive nature of events averred Ecclesiastes 1 verses 9 - 11; serving as the successful test of Ecclesiastes 1 verses 9 - 11 that I failed to conduct during my teenage years. Thus, I can say with a great measure certitude that: events keep repeating themselves over time. We fail to realize this, because when events repeat themselves, it is neither in the same environment, nor on the same plane. Therefore, whenever I'm trying to map future implications of certain events, I always look to the past - because the past abounds with rich answers to present-day questions.

President Barack Obama said in his inauguration speech that 'We'll begin to responsibly leave Iraq to its people'. When he said that, I thought that it is very noble of him to say that about Iraq. But how will the militant forces in Iraq react to a U.S. pull-out? I thus consulted history for the answer, and happened to stumble-across a riveting answer:

Every culture and religion has its own tales of a Robin-Hoodesque folklore hero. In early 20th century turbulent Mexico, the ideal personification of the Robin-Hood-legend was a fellow named Pancho Villa. During the Mexican Revolution of the early 1900s, he was the self-styled leader of a clique of bandits-cum-rebels that went around robbing trains, after which he would doll-out the proceeds of his daring raids to the impoverished masses. This won him the hearts of many, and his reputation for being tough but kind, spread far and wide. However, after some fierce battles, he lost his battle for absolute control to a gentleman named General Carranza, and retreated to a life of full-time banditry - which made him unpopular with the masses that once adored him. Being unloved infuriated Villa, and he hunted for a scape-goat.

He soon found one, the Americans, and went around butchering American soldiers and civilians alike (in some of the most gruesome ways); causing widespread trepidation and anger amongst American expatriates residing in Mexico. The American government was particularly infuriated by the acts of terrorism committed by Pancho, and deliberated on sending a military expedition to thwart Pancho. Therefore, the American government reasoned that it would be unwise for the United States not to strike back promptly, and that striking back would help to prop-up President Woodrow Wilson's image at home - as Americans largely perceived President Wilson as being; a pacifist/a schlep/a schmuck/unmanly/a wimp/ineffective/spineless/useless/heavily lacking in leadership and strength/a nebbish/K'vatsh. Hence, Wilson succumbed to the pressure, got permission from the Mexican government to capture Villa, and sent 10 000 troops to extract Villa from the wilds of Northern Mexico.

The Americans were poised for victory. They had with them the latest weaponry, and were supported by reconnaissance from the air. Also accompanying the Americans, was a small army of journalists which was strategically planted in different locations, as part of the PR campaign to bolster Wilson's image. However, things didn't play-out as the Americans envisaged. They were given false leads by Mexican civilians they paid for information; were despised by the peasantry in the Mexican country-side; navigated hostile terrain and unfriendly environmental conditions. Furthermore, Villa also succeeded in frustrating the extraction effort by playing cat and mouse with the US soldiers.

As the punitive effort continued to progress unsuccessfully, the American public grew restless, and was frustrated by the protracted war effort that was bleeding the fiscus. They started to view their government as inept, and started to respect Pancho as an astute man, who managed to escape the wrath of a superior force. This was a minus for the Wilson administration, which then decided to halt the punitive effort to prevent further humiliation.

When the U.S. force was pulling-out of Mexican territory, it was attacked and pursued by rebels. This forced the U.S. army to use planes to protect its vulnerable rear flanks. Therefore, the Obama government should be aware that U.S. forces stand a strong chance of being attacked heavily by militants when they pull out of Iraq. Hence, a quick withdrawal from Iraq is not the safest option to take, as it will expose U.S. forces to attack as they withdraw from Iraq.

Modeling the dynamics of economic distress caused by credit expansion

In his sagacious text entitled The New Paradigm for financial Markets: The Credit Crisis of 2008 and What it Means, the iconoclast speculator, George Soros, says that: "We are in the midst of the worst financial crisis since the 1930s. In some ways it resembles other crises that have occurred in the last twenty-five years, but there is a profound difference: the current crisis marks the end of an era of credit expansion based on the dollar as the international reserve currency. The periodic crises were part of a larger boom bust process; the current crisis is the culmination of a super-boom that has lasted for more than twenty-five years."

It is important to note that he unequivocally isolates unchecked credit expansion as the source of the unprecedented turmoil that has been roiling financial markets since August of 2007, i.e. he asserts that exponential credit expansion - which was a quintessential feature of capital markets during the last 25 years - is inextricably linked to the parlous financial condition the global economy currently finds itself in. Underlying the aggressive credit expansion that propelled the 25 year super-boom, was the revered and almost sacred Keynesian paradigm of macro-economic development; which asserts that aggregate demand has to be boosted through expansionary (policy) interventions, to alleviate an economy of recessionary pressures, which therefore revitalizes the economy, and puts it onto a growth trajectory.

Hence, some of the expansionary interventions that reserve banks (& other monetary authorities) use to assuage an economy of recessionary pressures are interest-rate cuts. When base interest rates are cut/reduced, credit becomes 'more-affordable', which in turn stimulates increased consumption, and leveraged investments by entities within an economy. Ostensibly, this has the consequential effect of stimulating aggregate demand - which results in economic growth, and promotes longterm economic stability.

Whilst it is logical to assume that cutting interest rates would stimulate increased consumption; which would in turn increase aggregate demand; thereby promoting economic stability and growth, empirical evidence discounts the assertion that interest-rate cuts can always be successfully used to stimulate longterm economic stability and growth. In fact, the market turmoil that was endured in 1987, and between 2007-2009 had its origins in the logically sound, but empirically unsound belief that interest-rate cuts can be used to stimulate longterm economic stability and growth. In fact, it can be said that interest rate cuts, whilst they might stabilize the economy in the short term, have a great likelihood of causing longterm instability in an economy with excess capital inflows and savings.

When the aforementioned crises were building-up, we witnessed an exponential growth in debt, caused by a borrowing and leveraging frenzy that was engendered by overly-low interest rates. Otherwise stated, the flood of 'cheap money' in the global economy during the build-up to both crises, fueled leveraged expenditures and investments that misallocated economic resources, which thus set the stage for the current dramatized market turmoil we are witnessing.

Therefore, in this post I'll attempt to illuminate on, using a conceptual model I developed, the dynamics of a crisis originating from unchecked credit expansion.

To be honest, I arrived at the model by pure accident when I was fudging around with a few abstract ideas. I have stripped from the model, the ugly mathematics that seems to put off a lot of people.

The graphical illustration below will be used to explain the dynamics of a crisis originating from unchecked credit expansion:

Explanation of the graphical illustration above:

• The illustration depicts the dynamics of an economy under distress owing to rapid credit expansion over time. Rates of change with respect to time (i.e. dx/dt, where x represents any of the six variables under consideration) are represented by the vertical axis, including the rate of change with respect to time of: Debt; Equity, GDP, The Debt-to-Equity ratio, The Base Interest Rate and The Natural Interest Rate. Time is represented by the horizontal axis. In the rest of this post, the phrase 'rate of change' will be used to mean 'rate of change with respect to time'.
  

• GDP: The rate of change of GDP (dGDP/dt) over time is represented by the lime-green trajectory labeled Z. Between point f and point g, the rate of change of GDP is negligible, although it does register a small net increase. From point g through to point s, the rate of change of GDP starts to register a steady decrease.

• Interest Rate: The rate of change of the base interest rate (di/dt) in the economy over time, i.e. rate of change of the risk-free rate, is represented by the grey/gray trajectory labeled U. The rate of change is somewhat stable - as evidenced by the general flatness of the trajectory - as base interest rates usually change at specific times of year - when monetary authorities announce new rates. On the diagram, an interest-rate downward movement is illustrated by the 'step-down' between points e and q on the grey/gray trajectory.
  

• Debt: The rate of change of the aggregate debt used by all agents in the economy (dd/dt) over time is represented by navy-blue trajectory labeled X. As evidenced by the trajectory between points a and e, the rate of change of debt usage in the economy grows exponentially, because of the abundance of 'cheap money' in the economy.
  

• Equity: The rate of change of the aggregate equity used by all agents in the economy (de/dt) over time is represented by red trajectory labeled Y. As evidenced by the negative gradient between points h and t, the rate at which equity is used to finance new activities of agents in the economy is falling. This generally indicates an increasing preference to use debt in the economy.
  

• Debt-to-Equity Ratio: The rate of change of the debt-to-equity ratio of the aggregated balance sheet of all agents in the economy (dde/dt) over time is represented by pink trajectory labeled W. As you can see from the trajectory between points j and n, the rate is increasing exponentially over time, faster than the rate at which usage of debt is increasing. This is because debt is growing at a fast rate, and equity is also falling at a fast rate, therefore the rate of change of the debt to equity ratio over time becomes steeper than the rate of change of the debt ratio over time for that reason (I shan't go into the mathematics of it).
  

• Natural Interest Rate: The rate of change of the natural rate of interest (dn/dt) over time is represented by the yellow trajectory labeled V. By the term 'natural rate of interest', I simply mean what the base rate of interest would be if it were left to be determined by the free market forces of supply and demand. As you can see from the trajectory between points p and t', the rate grows fast, but turbulently over time owing to the increasing demand for debt.

...The Dynamics of a credit-induced economic shock

To stimulate economic growth, monetary authorities reduce interests rates, as shown by the step between points e and q on the gray/grey trajectory labeled U. This causes the rate of change of the natural rate of interest to equal the rate of change of the base interest rate, as evidenced by the intersection at point q of the yellow trajectory labeled V and the grey/gray trajectory labeled U. This results in a material increase in GDP, as evidenced by the peak at point g on the green trajectory labeled Z, showing that credit expansion has had a positive impact on economic growth.

After that, the demand for credit grows at an astronomical rate - causing the natural rate of interest to gallop, as evidenced by the sharp increase of gradient between points q and t' on the yellow trajectory labeled V. At the same time, the base interest rate is fixed, meaning that the observed price of credit is cheaper than the perceived price of credit. Therefore, it becomes increasingly more beneficial for agents to finance their activities through debt as opposed to equity, which results in increasing usage of debt capital, as evidenced by exponential increase in the rate of debt usage depicted by the steep trajectory between points b and e on X, and a reduced usage of equity capital, as evidenced by the negative gradient between points i and t.

However, the flood of cheap money is having an adverse effect on economic growth, as evidenced by the steady decline of the rate of change of GDP between points g and e on the trajectory labeled Z. This means that the abundant credit money is increasingly being channeled to economically unproductive uses - a wastage of resources. Which sets the stage for economic collapse, as economic waste is unsustainable in the longterm.

On when the economic collapse will occur: that is tricky. But, it can occur at any point of time within what I term 'the crisis circle', shown by the blue circle in the illustration that connects points r, b, k, i , n, e, t'.

Hoping that you found the model useful.

Quantum Computing: Parallel Universes

Quantum Mechanics resonates well with me because it is the only science which has elements of the paranormal and mysticism embedded in it. To grasp it, one would have to adopt the mind of an iconoclast, and not only think in a queer way; but think in a way that is stranger than his/her native way of thinking.

The theory of quantum computing is especially mind-boggling, and furiously dizzying. Try to visualize in your mind 'parallel universes entangling to solve intractable problems'. It is hard - Isn't it?

Usually, if you posses an intuitive level of comprehension of quantum computing theory, you are either; mentally acute, and/or keenly imaginative, or just afflicted with a potent level of insanity (demented). I'd like to think that I fall into the keenly imaginative category, like the majority of the people who read Clive Staple Lewis' The Chronicles of Narnia in their juvenile years.

In the prequel of the series of The Chronicles of Narnia entitled The Magician's Nephew, Digory Kirke (the magician's nephew) and his new friend Polly Plummer enter into a 'portal land'/'central land'/'an in-between land', which has pools that lead to different worlds existing in parallel. Interestingly, the striking feature about all the lands they toggled back and forth from, is that they have unfathomably unique characteristics, and are abound with rich and endless adventures. Understandably, these are generally the flurry of images that are conjured up in the minds of most by the phrase parallel universes.

However, quantum computing, whilst riveting, is particularly bankrupt of the overflowing romance in The Chronicles of Narnia. Which begs the question of why the purveyors of quantum computing wisdom articulate the subject matter as if it were fantastical - like The Chronicles of Narnia. Their poor articulation of the subject matter, causes most people to misunderstand quantum computing; its capabilities; and, what it seeks to achieve.

From the outset, I must confess that I was one of the confused louts who misunderstood the florid phrase 'parallel universes entangling to solve intractable problems'. I comprehended it at a fantastical level (a.k.a as if it were The Chronicles of Narnia); instead of comprehending it at a more sedate realistic level. Obviously, I apportion most of the blame for my poor deconstruction of quantum computing theory, to poor articulation that is rife in many quantum computing research papers and articles. Another cause of this misinterpretation, albeit a minor one, is the keen imagination I nurture - which causes me to sometimes view things in a quixotic light. I only became clear about what the phrase truly meant, when I went through the quantum mathematics and quantum physics that underpins the theory of quantum computing.

In this post, I'll try to illuminate on what the pundits in the field of quantum computing mean by the phrase 'parallel universes entangling to solve computationally intractable problems'.

*******

Firstly, to understand the phrase 'parallel universes entangling to solve computationally intractable problems', it is important to de-construct the sentence into two key phrases, and to explain each phrase. Therefore, the key phrases in quote above are 'parallel universes' and 'entangling to solve computationally intractable problems'.

The hypothetical graphical illustration below will be used to explain both phrases:

Detailed explanation of the hypothetical graphical illustration: The illustration above shows the variability of the incomes of three groups of males over time; bankers, clerks and janitors. The horizontal axis represents time - incorporating all different flavors of the business cycle, and the vertical axis represents inflation adjusted income - meaning that all incomes under consideration are in 'constant dollar terms'. It is assumed in the illustration that income has a positive correlation to weight, height and I.Q. Thus, the adage underpinning this illustration is 'the higher the weight, height and I.Q. - the higher the income'. The sample of Bankers in this hypothetical case, has an average weight of 200lbs, is on average 6ft 1inch tall and has an intelligence quotient of 124 points. The sample of Clerks in this hypothetical case, has an average weight of 170lbs, is on average 5ft 11inches tall and has an intelligence quotient of 112 points. The sample of Janitors in this hypothetical case, has an average weight of 156lbs, is on average 5ft 6inches tall and has an intelligence quotient of 105 points. The Monte Carlo random run showing the cyclical variability of the incomes of Bankers is depicted by the navy-blue trajectory labeled A - which is the most turbulent; illustrating the high cyclical variability of a banker's income. In the illustration, the Monte Carlo random run showing the cyclical variability of the incomes of Clerks is depicted by the dark-green trajectory labeled B - which is more stable than A as evidenced by the smoother peaks and dips. Lastly, the Monte Carlo random run showing the cyclical variability of the incomes of Janitors is depicted by the lime-green trajectory labeled C - which is virtually flat, and is the most stable of all trajectories - indicating the 'cyclical-neutrality' of the incomes of janitors.

...Parallel Universes

The term 'universe' in statistics and logic simply means all objects a under consideration, or a population under consideration. In the graphical illustration in this post, there are three different discrete universes; A, B and C. Hence. it should be obvious now that in quantum computing jargon universe does not mean the cosmos, or all creation.

At time t1, the income of a banker is at1; a clerk is making bt1; and, a janitor is making ct1. Hence implying that at1 is parallel to bt1 and ct1 (at1 // bt1 // ct1), thereby implying that A is parallel to B and C (A // B // C). Therefore A, B and C are parallel universes. They are statistical observations related in that they explain different things happening at the same time to incomes of bankers, clerks and janitors. Not romantic like The Chronicles of Narnia at all!

...Entangling to Solve Intractable Problems

In the hypothetical graphical illustration above it is said that the vital statistics for bankers are: weight - 200lbs; height - 6ft 1 inch; I.Q. - 124. Clerks' statistics are: weight - 170lbs; height - 5ft 11 inches; I.Q. - 112. Janitors' statistics are: weight - 156lbs; height - 5ft 6 inches; I.Q. - 105.

Now, suppose that you are asked to map the cyclical variability (over time) of the income of a banker who weighs 200lbs, is 5ft 11 inches tall and has an I.Q. of 105 - a banker who's not represented by the universe labeled A: who has the weight of someone in the A universe; the height of someone in the B universe; and, the I.Q. of someone in the C universe. Someone who's the amalgam of specific individual characteristics of A, B, and C groups. What would you do?

I would average the each income observation of people in the A, B and C groups (i.e. [atx + btx+ ctx]/3) to derive each point of the trajectory illustrating the cyclical variability of the income of the atypical banker over time. However, that is a very crude way of solving the problem.

Height, Weight and I.Q., may not have an equal influence on income, and thus, I'd need to find the level of correlation between weight/I.Q./height and income, and factor that into my 'averaging',

A quantum computer can solve a more complex type of that problem (in the correct way) - with hundreds and thousands of universes, by taking each vital characteristic of each universe - taking into consideration the weighted impact the characteristic has on the point of interest; and blending it into the computational process to derive the end solution - at a frightening level of accuracy, and instantaneously. Hence the phrase parallel universes entangling to solve intractable problems.

Do you still think that quantum computing is romantic?

I don't.

The eBay, or Google of the future

In his 1993 essay titled The Coming Technological Singularity: How to Survive in the Post-Human Era, mathematician Vernor Vinge suggested that technology may in the future, create entities with greater than human intelligence by interconnecting a grid of computers, which consequently gains consciousness and wakes up as a superhumanly intelligent entity.

At that time, the internet and networking technologies weren't intertwined into every facet of our lives as they now are, and people largely dismissed his assertion as the quixotic and fantastical utterances of an aging mathematician.

Fast-forward sixteen years, we are in 2009, and 1.574313184 billion people (~23.5% of the world's population) now use the internet. The computing power that was once commanded by servers that would fill a room the size of a football pitch, is now commanded by hand-held devices and ordinary desktop computers. The cost-price-efficiency of computers is increasing exponentially, in accordance with Moore's Law, and we'll soon reach a time when individuals/institutions are in possession of more computational power than they could ever use/need. Hence, the question: What do we do with our excess computing power?

The field of wealth management came into existence when people who had excess money came to the realization that they could make their excess money work to generate even more money, thus, exponentially growing their wealth. Similarly, I think that now (more than ever), people with excess computational power need opportunities to put it to work; enabling it to generate something that people have an insatiable appetite for: money.

Unfortunately, the global capitalist economic system has been slow to respond to this need, and this may hinder progress in academical research, medicine, science, defense, web-based applications, and quantitative finance - disciplines that have a perennial demand for more computational power than is offered by the currently-reigning top super-computers. The demand for computational power is existent and the supply of computational power is growing exponentially. What is currently missing, is a market-place, like eBay, that can bring buyers and sellers of computational power together, in a safe environment.


...Wastage of Resources

Unfortunately, a lot of venture capitalists choose to waste valuable resources by investing in online social networking companies. They fail to realize that the economic benefits of investing in social networking start-ups vanished completely when Facebook was created. Facebook is a social platform that allows its users to generate content and to create diverse 'ecosystems' within the platform practically free of charge. Hence, this implies that the platform evolves with the diversity of its user-base, and continually becomes like its user-base in terms of aggregate characteristics.

Thus, as time progresses, Facebook will cater to every conceivable genre of online social networking needs, through applications and groups hosted on the site. This will render obsolete many of the social networking sites in existence today, as most lack the diversity of user-base, and 'user-empowering' features that Facebook has. Therefore, it makes no sense for prudent venture capitalists to continue investing in social networking start-ups, as Facebook has a design philosophy which guarantees it a growing lion's share of the social networking market. Facebook is one of the most disruptive companies in the world, and it will dramatically alter the social networking space in ways we cannot fathom.


...The Googles of the Future

Therefore, venture capitalists must now search for opportunities that will yield them exponential returns. Thus, it is my belief that a 'grid networking' market that brings together the buyers and sellers of computational power in a secure environment, is one of the biggest opportunities they can find.

I think that the Googles and eBays of the near-future have the greatest likelihood of emerging from the field of grid computing, and now, venture capitalists and entrepreneurs need to position themselves for the next big thing, and stop wasting their time and resources on social networking companies.

To those who doubt this assertion, think about this: DWave Systems, a start-up that is producing quantum computing hardware and software solutions, is currently seeking volunteers who'll donate computing resources (read: processor time) to test adiabatic quantum algorithms through a distributed computing grid. The concept of 'others using your computing resources' is already in existence, but it now needs to be monetized through a robust business model that will add value to society.

Understanding Market Behavior

As the world greeted the new year - 2009, I listened to New York State Insurance Department Superintendent - Eric Dinallo's Bloomberg interview with the ever-zippy Tom Keene. In the interview, Superintendent Dinallo said something that made me freeze and ruminate for a while: "You can't ask VaR (Value-at-Risk) first-order questions like 'Are we in a credit bubble?'. That is not a question you can ask VaR formulae."

What specifically caught my attention was the part where he said "Are we in a credit bubble?" I kept asking myself 'How can we establish whether we are in a bubble, or not?'. At that time, my knowledge on asset bubbles was chiefly influenced by the writings of Professor Robert J. Shiller, author of Irrational Exuberance. Hence, I naturally arrived at the conclusion that predicting, or knowing whether a speculative bubble is being inflated in your midst is only easy with hindsight - an assertion Shiller makes on countless occasions.

However, new insights I've gained since then, are challenging that conclusion.

A speculative bubble morphs over time like human beings, from an 'embryonic stage'; to infancy; to a juvenile stage; to adolescence; to maturity - 'the adulthood stage'; to the stage of decline - the equivalent of 'aging' in human beings; and, eventually death - when the bubble explodes, or bursts. Ascertainment of the existence of an asset price bubble, is difficult when a bubble is still at an embryonic stage, but it becomes easier with each progressive stage of maturity the bubble enters. Hence, I believe that I have found a way to establish if an asset price bubble that has been inflated is about to burst - i.e. if the bubble is making a transition from its 'aging phase' to its 'death phase', specifically in stock markets, and that can be done by examining the behavior of growth stocks and value stocks over time.

In their paper series on The Anatomy of Value and Growth Stock Returns, Eugene Fama and Kenneth R. French did a study of value stocks and growth stocks, between 1927-2006 - a period of 79 years, and found that value stocks outperform growth stocks over two-thirds of the time (which translates to ~ > 52.667 years, or 66.667% of the time) during that period, which in turn implies that growth stocks outperform value stocks one third of the time (which translates to ~ less than 26.333 years, or 33.333% of the time). Clifford Asness, the Principal of AQR, sums this observation as: "Cheap beats expensive more than it should.''

My belief is that stock price bubbles can be understood better, when people carefully scrutinize the periods when highly volatile growth stocks outperform highly volatile value stocks, because I believe that stock price bubbles lie within those time periods.

Hence, I suspect that when a portfolio of highly volatile growth stocks consistently outperforms a portfolio of highly volatile value stocks; a stock price bubble may be in your midst. To ascertain if the bubble is about to burst one would have to ascertain the differences between the rates of change of value both portfolios - with respect to time, and when that difference is at its greatest, it is a sign that the stock price bubble is ab0ut to burst.

Mathematically the last section preceding paragraph can be expressed as:

The bubble is about to burst when:

Where:

Max means the maximum
dAVg/dt is the rate of change of the value of a portfolio of growth stocks with respect to time
dAVv/dt is the rate of change of the value of a portfolio of value stocks with respect to time

Let's test that hypothesis to establish how right/wrong I am.

Possible way of modeling the 'contagion effect' in Financial Markets (Part 4)

...Continued from Part 3

The last equation from Part 3, i.e. (A1.7) is soluble by standard methods to give the analytical solution:

Where:

And also:

When you graph (A1.8), you get a curve that looks something like this:

Comment on Hypothetical Graphical Illustration depicting the relationship between R (the removals) and t (time) inferred by equation (A1.8): When the crisis commences, the number of removals in the hedge fund sub-community grows exponentially as shown by the trajectory between point a and point b in the graph above. The removal rate then slows down somewhere after point b, and levels out between point b and point c. Between points c and d, the rate of removals gradually, albeit negligibly, slows down, until it falls steeply between points d and points e. At point e, there are no more removals and the crisis would have 'ended'. When deriving a numerical solution, using the Runge-Kutta-Fehlberg (R-K-F) algorithm, which is very efficient in that it only requires six evaluations per step, the errors are larger when the graph is at steepest descent, i.e, between points d and point e. Therefore, as dR/dt → -∞ , the accuracy of the model diminishes. The general rule is: 'the higher the infection rate the steeper the curve'. Furthermore, the higher the infection rate the shorter the time period required for the number of removals to level out. Clearly higher infection rates lead to higher values of R∞ (see equation (A1.12) for more details on R∞).

Therefore, the curve illustrating the rate of 'removals' in the hedge-fund industry with respect to time is given by the following equation, which in essence is the equation for computing the gradient of the Hypothetical Graphical Illustration depicting the relationship between R (the removals) and t (time) inferred by equation (A1.8) :

Computing the maximum casualty count is achieved by taking the limit of the contagion effect as t →∞ in equation (A1.8) which gives the equation for approximating the maximum casualty count as:

In the Hypothetical graphical illustration of equation (A1.8), the maximum casualty count is shown by the 'leveled-out' section of the trajectory between points b and c

...Fitting the model into an existing Risk Management Framework

Risk management is more of an art than a science, and the best way to use this tool is to generate multiple random paths or random runs (Monte Carlo Simulation), starting at a hypothetical crisis 'commencement' date (to) and ending at another fixed date that is randomly selected, or 'picked' strategically. A real life 'infection-rate' β can be computed using real-life data, and other inputs for the model, like number of susceptible funds and the number of funds under stress at the specific time can be plugged-in from real-life data sources, or, hypothetical inputs can be generated if the risk manager choses to do that. To generate the random sample paths/random runs from the commencement date, the 'infection rate' and its components (e.g. leverage, correlation, e.t.c.) can be fudged around with, using a 'random' number generator. The multiple sample paths, are in essence, scenarios, that can be classed in from the worst case, to the best case scenarios, for detailed analysis. The most important thing to look-out for, are prevalent characteristics features of all sample paths - they will tell you what you need to know about your vulnerability to being wiped-out by the contagion effect.

Hopefully, you'll find this model as useful as I did.

-The End-

Please Note: This model is inspired by a paper co-authored by Jim Caldwell and Kei Shing Ng, titled: Deterministic Model in Contagious Disease, and is going through a continual overhaul to make it more robust. So far I've had this model critiqued by Rick Bookstaber, author of A Demon Of Our Own Design: Markets, Hedge Funds And The Perils of Financial Innovation, and he highlighted a lot of flaws, in the model and its presentation, that I'm currently addressing. Dr. Ernest Chan, the author of a quantitative text titled Quantitative Trading: How to Build Your Own Algorithmic Trading Business is also in the process of critiquing the model, and I'll also take his opinions on board. Furthermore, Dr. Jim Caldwell, the originator of the model I drew analogies from, also gave me a few pointers on how to make the model more realistic, and I'll also be taking his pointers on board. I also benefited from Eric Falkenstein's critique of the model, and I will be taking his suggestions on board as well. Please stay tuned!

Possible way of modeling the 'contagion effect' in Financial Markets (Part 3)

...Continued from Part 2

Mathematical/Numerical Solution

We now consider the analytical solution of equations (A1.4)-(A1.6). By eliminating I from equations (A1.4) and (A1.6), we have:

Integration yields:

Which can be expressed as:

When t = 0:

And thus,

S=So=A

Since I=n−S−R, equation (A1.6) becomes:

As:

The right-hand side of the equation above can be expanded as far as the term in R squared to give:


Stay tuned for Part 4

Please Note: This model is inspired by a paper co-authored by Jim Caldwell and Kei Shing Ng, titled: Deterministic Model in Contagious Disease, and is going through a continual overhaul to make it more robust. So far I've had this model critiqued by Rick Bookstaber, author of A Demon Of Our Own Design: Markets, Hedge Funds And The Perils of Financial Innovation, and he highlighted a lot of flaws, in the model and its presentation, that I'm currently addressing. Dr. Ernest Chan, the author of a quantitative text titled Quantitative Trading: How to Build Your Own Algorithmic Trading Business is also in the process of critiquing the model, and I'll also take his opinions on board. Furthermore, Dr. Jim Caldwell, the originator of the model I drew analogies from, also gave me a few pointers on how to make the model more realistic, and I'll also be taking his pointers on board. I also benefited from Eric Falkenstein's critique of the model, and I will be taking his suggestions on board as well. Please stay tuned!

Possible way of modeling the 'contagion effect' in Financial Markets (Part 2)

...Continued from Part 1

Obviously, if the 'blow-ups' are removed from the hedge-fund community, they will not be in contact with the susceptibles group. Therefore, the number of susceptible hedge funds is only proportional to both the number of infected hedge-funds and the number of susceptibles, and so we have:

However, the removals (i.e the blow-ups) should be considered in the differential equation for the number of infected hedge funds i.e equation (A1.2), which should be modified to:

The equation for the number of hedge funds removed from the infectives with removal rate γ then becomes:

At the start of the crisis, when t = 0 , we assume that there are no removals, a very small number of infectives, Io , and the remaining population is susceptible, S, which is approximately equal to n. Thus, at t = 0, (S,I,R) take the values (So,Io,0). For convenience, we make use of
μ = γ/β, as the relative removal rate.

From equation (A1.5), it follows that unless μ is less than So there will not be a crisis the in hedge-fund sub-group as [dl/dt]t=0 is required to be greater than zero. On the other hand, for the case μ > So, the number of affected hedge-funds will be increasing. Therefore, the relative removal rate, μ = So , gives a threshold density of susceptibles.

Stay tuned for Part 3


Please Note: This model is inspired by a paper co-authored by Jim Caldwell and Kei Shing Ng, titled: Deterministic Model in Contagious Disease, and is going through a continual overhaul to make it more robust. So far I've had this model critiqued by Rick Bookstaber, author of A Demon Of Our Own Design: Markets, Hedge Funds And The Perils of Financial Innovation, and he highlighted a lot of flaws, in the model and its presentation, that I'm currently addressing. Dr. Ernest Chan, the author of a quantitative text titled Quantitative Trading: How to Build Your Own Algorithmic Trading Business is also in the process of critiquing the model, and I'll also take his opinions on board. Furthermore, Dr. Jim Caldwell, the originator of the model I drew analogies from, also gave me a few pointers on how to make the model more realistic, and I'll also be taking his pointers on board. I also benefited from Eric Falkenstein's critique of the model, and I will be taking his suggestions on board as well. Please stay tuned!

Possible way of modeling the 'contagion effect' in Financial Markets (Part1)

'Contagion is best defined as a significant increase in cross-market linkages after a shock to an individual country (or group of countries), as measured by the degree to which asset prices or financial flows move together across markets relative to this co-movement in tranquil times.'

— Rudiger Dornbusch, Yung Chul Park, Stijn Claessens in their research paper titled Contagion: Understanding How It Spreads

A lot has been written on the 'contagion effect' in financial markets, but to my disappointment there hasn't been much written on how to model the dynamics of the financial market contagion effect. Therefore, I rummaged through most of the reputable biological journals I could find, in search of key insights about modeling the 'contagion effect' of diseases that afflict biological organisms. My initial hope was that if I found something 'good', I would draw analogies from it, to assist in the calibration of the contagion effect in financial markets.

As luck would have it, I found a deterministic model for calibrating the potential effects of a contagious virus on a human population in a paper, by Jim Caldwell and Kei Shing Ng, titled: Deterministic Model in Contagious Disease, which this post heavily draws analogies from. The original logical format and the notation of their work is preserved, with of course slight adjustments made, to make the model relevant to the matter of discussion, which in this case is the contagion effect in financial markets. Therefore, I must point-out from the onset that I am just a translator, not an originator of this model - I'm just adapting it to make it relevant to financial markets.

The model in this post is the ensemble of equations which describe and interrelate the variables and parameters of a physical system - which in this particular case, is a hedge-fund sub-sector under conditions of distress that originate from a few individual funds within the sub-sector, and eventually cascade throughout the whole sub-sector through the contagion effect.

Whilst this model may lack robustness, it is my belief that it is a concrete starting point, for formulation of a robust risk management tool that explains the dynamics of the contagion effect, and will hopefully help industry players to mitigate systemic risks that stem from their individual activities.

...The Model

From the outset, I have to mention that I designed the model from the perspective of a fund-manager, who wants to know how vulnerable he is to being wiped-out because of the effects of stresses that may be affecting other funds with an operational strategy similar to his.

I consider here a (relatively) homogeneously mixed group of hedge-funds, i.e hedge-funds with a common operational strategy and overlapping portfolios, of size n+a under the assumptions that initially a individuals individuals are under conditions of stress with the remaining n individuals all being susceptible, but not yet 'infected' by the stress. This leads to the following classical basic model:

Let time t be the independent variable, I(t) and S(t) be continuous, where:

S(t) = number of susceptible funds at time t, and:
I(t) = number of funds under stress at time t

The key assumption of this model is that the rate of occurrence of new infections (i.e the rate at which the stress spreads the other funds) is proportional to both the number of infectives (i.e funds already under stress) and the number of susceptibles (i.e funds with a high likelihood of experiencing the stress through the contagion effect owing to a portfolio overlap with the infected funds and the use of leverage), we can write:

I(t+Δt) = I(t) + βI(t)S(t)Δt (A1.1)

Where: β = infection rate (or contact rate). β is directly proportional to the average percentage of leverage (in relation to NAV) used by the affected hedge-fund sub-population, which is denoted by the letter q, and, β is also directly proportional to the level of portfolio overlap between the hedge-funds, which in this case is measured by computing the average level of correlation between the funds' portfolios and the index that tracks the performance of funds in the specified strategy(ies), denoted by the letter v. β is also directly proportional to the average volatility of the overlapping portfolio, or the most common basket of securities in the portfolios of different funds operating in susceptible hedge fund sub-community, which in this case is denoted by the letter e. Furthermore, β is also directly proportional to the aggregate amount of redemption requests as a percentage of aggregate AUM of all affected and susceptible funds, which in this case is denoted by the letter j. Therefore Mathematically expressed:

β = k.qvej, where k is a constant.

Therefore, the equation (A1.1) reads; the cumulative number of funds under stress during the current time period I(t+Δt) is equal to the sum of the cumulative number of funds under stress during the last time period I(t) AND the product of: the infection rate β; the cumulative number of funds under stress during the time period before the current one I(t); the cumulative number of susceptible funds during the time period before the current one S(t), and the time that has elapsed between the previous time period and the current time period Δt.

In the limit as Δt→0 , this yields:

With initial conditions S(0) =n, I (0) = a

In addition, since the total population size is always n + a, and all individuals are either susceptible or infected, it is clear that S(t) + I(t) = n + a for all t , which means that:

S(t) = n + a - I(t) and when you put n+a - I(t) in (A1.2) in the place of S(t) it follows that:



Whenever there is a shock in financial markets, there are bound to be casualties (blow-ups), that reduce the population of hedge funds in general. To make our original model more realistic, we can extend it by including a third variable R(t) to represent the number of hedge funds that are removed from the affected population at a given time t.

Therefore, the following assumptions are made for this model: The removals include infectives who are dead or recovered and immune; The immune or recovered removals enter a new class which is no longer susceptible to the stressing condition.

Hence, let R(t) = the number of removals at time t and γ is the removal rate, which in this case is partially comprised of the observed rate of bankruptcy of affected hedge funds owing to the prevailing condition of stress - such that we now have:

I(t) + S(t) + R(t) = n,

Where n is the total size of the affected hedge fund sub-community (i.e the strategy to which affected funds belong to).

Stay tuned for part 2.

Please Note: This model is inspired by a paper co-authored by Jim Caldwell and Kei Shing Ng, titled: Deterministic Model in Contagious Disease, and is going through a continual overhaul to make it more robust. So far I've had this model critiqued by Rick Bookstaber, author of A Demon Of Our Own Design: Markets, Hedge Funds And The Perils of Financial Innovation, and he highlighted a lot of flaws, in the model and its presentation, that I'm currently addressing. Dr. Ernest Chan, the author of a quantitative text titled Quantitative Trading: How to Build Your Own Algorithmic Trading Business is also in the process of critiquing the model, and I'll also take his opinions on board. Furthermore, Dr. Jim Caldwell, the originator of the model I drew analogies from, also gave me a few pointers on how to make the model more realistic, and I'll also be taking his pointers on board. I also benefited from Eric Falkenstein's critique of the model, and I will be taking his suggestions on board as well. Please stay tuned!